Finally, you say that "Myself and Yankee have both written at length about how antislavery does not necessarily equal liberalism", which I agree with. In fact, I'm arguing against the same sort of ideological absolutism as you are, the notion that anti-Catholicism necessarily equals conservatism. Because the truth, whether you like it or not, is that anti-Catholicism has long been a major part of Anglo-American left radicalism. Was Paul Blanshard, the socialist author and Nation editor who wrote American Freedom and Catholic Power, a conservative? Perhaps he was misguided or simply wrong, but he was following in a recognizably left-wing anti-Catholic tradition dating back 3 centuries before his book was published.
I was having a discussion about this with some conservative posters on discord, people who are more knowledgeable on religious matters. A point was made to me about the fact that regardless of the group in question, Americans of various different groups alledged to be part of some international political alignment against the principles of the US, often tend to lack such allegiance despite the best claims of any number of groups hostile to their presence.
American Catholics were by and large not taking orders from Rome, just like millions of German-Americans fought in the American Army in WWII along with numerous Italians and Japanese (even as their families were horribly abused and interned).
Most people after moving to America, have become Americanized and their allegiance is to the principles of the United States. For all of the bemoaning of Catholics, and discussions of pro-Republican trends among Catholics in the 20th century, vast numbers of Catholics were essential to the elections of FDR, Truman, JFK, were critical to the successes of Civil Rights, the enactment of the New Deal and such forth. Trends are just that, a smaller percentage becomes a larger percentage, but its not 100% to 0%, its 40% becomes 60% or in the case of Catholics as a group probably 25% becomes 50%. As recently as the 2000s, Catholics were a swing group nationally.
The first Catholics to become Republicans and remain so, were ones who had the means to not be concerned about surviving to the next paycheck. Middle Class, professionals, small business owners and bonus points if they left the city and its machine's reach for the suburbs. Beyond that towards the later part of the 20th century, it became more of a religiousity skew as opposed to a wealth skew. This is not because they were taking orders from the Pope, but because they saw the Protestant zeal of the Republicans a more befitting ally than the secular liberalism of the Democrats.
Religiosity as it relates to political identity is not generated because of what the religious is, or even what its teachings are, but by the perceived regard in which they are held by the dominant or "perceived" dominant view on religion. In the late 20th century and onwards, increasingly the dynamic was the more religious, the more Republican because religious people (certainly so towards the more recent period) see a dominant secular establishment that is hostile their interests and that which dominates the Democratic Party. By the same token, many groups were alarmed and still are alarmed by the perceived power held by the Evangelical community and their influence within the Republican Party.
While these writers and thinking types are relevant to understand the justifications and such, as I have repeatedly stated, I think the power dynamic comes first and then often times the justification is either appropriated or created to justify it afterwards, which explains any number of incoherent positions seemingly held by the parties. They are collections of interest groups, operating within and against various power dynamics and the academic types merely serve to provide a basis for these seemingly random combinations. Republicans want smaller government, but a larger military etc.
I don't want to come across as completely discounting these writers, but when we are especially talking about a period where most Americans were more concerned about how they are going to eat tomorrow, their opinion is not motivated by what some "writer drawing on 300 years of tradition is saying". Their opinion is motivated by who they think is causing their pain and for the nativist, it is the immigrants taking their jobs. For the Whig patronage worker, it is the immigrant voting their political meal ticket out of office. These writers, thinkers and the politicians who would cite them to justify their actions, are really just coopting the 95% motivated by the above relative power dynamics and generally, I tend to think they are more important to consider when understanding political history.